{"title":"伪树上的图索引随机漫步","authors":"Jan Bok , Jaroslav Nešetřil","doi":"10.1016/j.endm.2018.06.045","DOIUrl":null,"url":null,"abstract":"<div><p>We investigate the average range of 1-Lipschitz mappings (graph-indexed random walks) of a given connected graph. This parameter originated in statistical physics, it is connected to the study of random graph homomorphisms and generalizes standard random walks on <span><math><mi>Z</mi></math></span>.</p><p>Our first goal is to prove a closed-form formula for this parameter for cycle graphs. The second one is to prove two conjectures, the first by Benjamini, Häggström and Mossel and the second by Loebl, Nešetřil and Reed, for unicyclic graphs. This extends a result of Wu, Xu, and Zhu [5] who proved the aforementioned conjectures for trees.</p></div>","PeriodicalId":35408,"journal":{"name":"Electronic Notes in Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2018-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.endm.2018.06.045","citationCount":"2","resultStr":"{\"title\":\"Graph-indexed random walks on pseudotrees\",\"authors\":\"Jan Bok , Jaroslav Nešetřil\",\"doi\":\"10.1016/j.endm.2018.06.045\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We investigate the average range of 1-Lipschitz mappings (graph-indexed random walks) of a given connected graph. This parameter originated in statistical physics, it is connected to the study of random graph homomorphisms and generalizes standard random walks on <span><math><mi>Z</mi></math></span>.</p><p>Our first goal is to prove a closed-form formula for this parameter for cycle graphs. The second one is to prove two conjectures, the first by Benjamini, Häggström and Mossel and the second by Loebl, Nešetřil and Reed, for unicyclic graphs. This extends a result of Wu, Xu, and Zhu [5] who proved the aforementioned conjectures for trees.</p></div>\",\"PeriodicalId\":35408,\"journal\":{\"name\":\"Electronic Notes in Discrete Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2018-07-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/j.endm.2018.06.045\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Electronic Notes in Discrete Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S1571065318301367\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Electronic Notes in Discrete Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1571065318301367","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"Mathematics","Score":null,"Total":0}
We investigate the average range of 1-Lipschitz mappings (graph-indexed random walks) of a given connected graph. This parameter originated in statistical physics, it is connected to the study of random graph homomorphisms and generalizes standard random walks on .
Our first goal is to prove a closed-form formula for this parameter for cycle graphs. The second one is to prove two conjectures, the first by Benjamini, Häggström and Mossel and the second by Loebl, Nešetřil and Reed, for unicyclic graphs. This extends a result of Wu, Xu, and Zhu [5] who proved the aforementioned conjectures for trees.
期刊介绍：
Electronic Notes in Discrete Mathematics is a venue for the rapid electronic publication of the proceedings of conferences, of lecture notes, monographs and other similar material for which quick publication is appropriate. Organizers of conferences whose proceedings appear in Electronic Notes in Discrete Mathematics, and authors of other material appearing as a volume in the series are allowed to make hard copies of the relevant volume for limited distribution. For example, conference proceedings may be distributed to participants at the meeting, and lecture notes can be distributed to those taking a course based on the material in the volume.
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